Aad van der Vaart教授是当今具有国际声望的统计学家，是荷兰皇家艺术与科学院院士。他在经验过程和半参数统计方面做出过重要的基础性贡献，所著Weak Convergence and Empirical Processes (1996, 与Jon Wellner合著) 和Asymptotic Statistics (1998) 已成为这一领域的经典文献和必读书目。近年来他的兴趣主要集中在非参数贝叶斯方法、高维统计及统计遗传学、复杂网络等应用领域。Aad van der Vaart studied mathematics, philosophy and psychology at the University of Leiden, and received a PhD in mathematics from this university in 1987. He held positions in College Station, Texas and Paris, held a Miller fellowship in Berkeley, and was visiting professor in Berkeley, Harvard and Seattle. Following a long connection to the Vrije Universiteit Amsterdam he is currently Professor of Stochastics at Leiden University. He is a member of the Royal Netherlands Academy of Arts and Sciences. His research has been funded by NWO, VU-USF, STW, CMSB, NDNS+, STAR, and most recently by the European Research Council (ERC Advanced Grant, 2012). He received the C.J. Kok prize in 1988, the van Dantzig award in 2000, and the NWO Spinoza Prize in 2015.Aad van der Vaart's research is in statistics and probability, as mathematical disciplines and in their applications to other sciences, with an emphasis on statistical models with large parameter spaces. He wrote 6 books and 18 lecture notes (on topics such as empirical processes, time series, stochastic integration, option pricing, statistical genetics, statistical learning, Bayesian nonparametrics), as well as over 130 research papers.Aad van der Vaart was associate editor of the Annals of Statistics, Statistica Neerlandica, Annales de l'Institut Henri Poincare, Probability Theory and Related Fields, co-editor of Statistics and Decisions, and is currently associate editor of Indagationes Mathematicae, Journal of Statistical Planning and Inference and ALEA. Keynote lectures include the Forum Lectures at the EMS 2009, the Le Cam lecture at the JSM 2009, invited address at the International Congress of Mathematicians in 2010, a foundational lecture at the world meeting of International Society for Bayesian Analysis in 2012, the Hotelling lectures in 2017 and the Barrett lectures in 2017. He was program chair for the European Meeting of Statisticians 2006 in Oslo and BNP10 (2015) in Raleigh, and local chair of BNP9 and the European Meeting of Statisticians 2015. Among former administrative functions are president of the Netherlands Society for Statistics and Operations Research (2003-07), head of the Department of Mathematics of VU University (2002-06), chair of the European Council of the Bernoulli Society, scientific chair of the Stieltjes Institute, chair of the mathematics board of the Lorentz Centre, board member of the NDNS+ and STAR clusters, and council member of the International Statistical Institute. He is currently council member of the Institute of Mathematical Statistics and member of the steering committee of the Statistical Science master in Leiden. Since September 2015 he is Scientific Director of the Mathematical Institute of Leiden University.

课程内容简介

In the Bayesian statistical paradigm a prior probability distribution on the parameter space is updated to a posterior probability distribution after seeing the data. The latter is simply the conditional distribution of the parameter given the data, based on viewing the likelihood as the conditional distribution of the data given the parameter. In nonparametric statistics the parameter is an infinite-dimensional object, such as a function or a distribution, and the prior is a probability distribution over the appropriate infinite-dimensional space. In high-dimensional statistics the parameter space is Euclidean, but there are typically more parameters than observations. A large variety of prior distributions have been developed, usually together with algorithms to simulate from the posterior distribution. In this course we shall consider the Dirichlet process and Dirichlet mixtures, Gaussian process priors, and the spike-and-slab and horseshoe priors for sparse high-dimensional models, among others. We shall further mostly be concerned with the question if Bayesian inference with these priors 'works'. This entails two main desirables. First one would like that a posterior distribution concentrates most of its mass near the 'true' parameter if in reality (and deviating from the Bayesian assumption) the data were sample according to this true parameter. This property can be captured by a contraction rate (if any) of the posterior distribution as the informativeness of the data (e.g. the number of observations) increases indefinitely. Second one would like that the spread of the posterior distribution can be interpreted somewhat in the same fashion as the width of confidence sets. We shall see that the desirables are met by large classes of priors, but that, unlike for finite-dimensional models, the prior does play an important role in the asymptotics. Families of priors with a tuning parameter (bandwidth, smoothness, sparsity level, etc.), which can itself be equipped with a prior or estimated by empirical Bayes, are especially attractive.